US5825810A  MSK spreadspectrum receiver which allows CDMA operations  Google Patents
MSK spreadspectrum receiver which allows CDMA operations Download PDFInfo
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 US5825810A US5825810A US08770224 US77022496A US5825810A US 5825810 A US5825810 A US 5825810A US 08770224 US08770224 US 08770224 US 77022496 A US77022496 A US 77022496A US 5825810 A US5825810 A US 5825810A
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 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04B—TRANSMISSION
 H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00  H04B13/00; Details of transmission systems not characterised by the medium used for transmission
 H04B1/69—Spread spectrum techniques
 H04B1/707—Spread spectrum techniques using direct sequence modulation

 H—ELECTRICITY
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 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L27/00—Modulatedcarrier systems
 H04L27/18—Phasemodulated carrier systems, i.e. using phaseshift keying includes continuous phase systems
 H04L27/22—Demodulator circuits; Receiver circuits
 H04L27/233—Demodulator circuits; Receiver circuits using noncoherent demodulation
 H04L27/2332—Demodulator circuits; Receiver circuits using noncoherent demodulation using a noncoherent carrier
Abstract
Description
This patent is a continuation of U.S. patent application entitled, MSK SPREADSPECTRUM RECEIVER WHICH ALLOWS CDMA OPERATIONS, having Ser. No. 08/324,478 and filed Oct. 17, 1994, now U.S. Pat. No. 5,592,506. The benefit of the earlier filing date of the parent patent application is claimed pursuant to 35 U.S.C. § 120.
This invention relates to spreadspectrum communications, and more particularly to an minimum shift keyed (MSK) receiver which can be used in a code division multiple access (CDMA) spreadspectrum communications environment.
Using MSK modulation is desirable because this type of modulation has a constant envelope signal and can be used with a more efficient Class C amplifier. Also, signals using MSK modulation have a steeper outofband signalenergy rolloff, which reduces interference to adjacent channels. Unfortunately, the use of conventional frequency modulation (FM) discriminators in a typical MSK receiver creates a nonlinearity before the spreadspectrum codeword digital correlators. CDMA operation with an MSK receiver using an FM discriminator is therefore not desirable.
A general object of the invention is an MSK receiver which can receive spreadspectrum signals.
Another object of the invention is an economical approach to receiving spreadspectrum signals.
According to the present invention, as embodied and broadly described herein, an MSK receiver and method is provided for receiving spreadspectrum signals. The method comprises the steps of generating an inphasecomponent signal and a quadraturephasecomponent signal from the receivedspreadspectrum signal; processing the inphasecomponent signal using sin_{doub} S(n,C) to generate a first processed signal, and using cos_{doub} S(n,C) to generate a third processed signal; processing the quadraturephasecomponent signal using sin_{doub} S(n,C) to generate a second processed signal, and using cos_{doub} S(n,C) to generate a fourth processed signal.
For noncoherent reception, the third processed signal is combined with the second processed signal to generate a first combined signal, and the third processed signal is combined with an inverse of the second processed signal to generate a second combined signal. The first processed signal is combined with the fourth processed signal to generate a third combined signal, and an inverse of the first processed signal is combined with the fourth processed signal to generate a fourth combined signal. From the first combined signal, the second combined signal, the third combined signal and the fourth combined signal, the method determines an estimate of the data contained in the receivedspreadspectrum signal.
For differentially coherent reception, the method combines the third processed signal with the second processed signal to generate a first combined signal. The inverse of the first processed signal is combined with the fourth processed signal to generate a second combined signal. An angle is determined from the first combined signal and the second combined signal. From the angle the method determines an estimate of the data contained in the receivedspreadspectrum signal.
For differentially coherent reception of special type of codewords, the third processed signal and the fourth processed signal need not be generated. Instead, the method combines a delayed version of the first processed signal with an inverse of the second processed signal to generate a first combined signal, and combines the first processed signal with a delayed version of the second processed signal to generate a second combined signal. An angle is determined from the first combined signal and the second combined signal. From the angle the method determines an estimate of the data contained in the receivedspreadspectrum signal.
Additional objects and advantages of the invention are set forth in part in the description which follows, and in part are obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention also may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.
The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate preferred embodiments of the invention, and together with the description serve to explain the principles of the invention.
FIG. 1 illustrates a model of a spreadspectrum CDMA system with MSK modems;
FIG. 2 is a phase state diagram;
FIG. 3 is a block diagram of an MSK noncoherent average chip phase receiver;
FIG. 4 is a block diagram of a differentially coherent spreadspectrum MSK receiver;
FIG. 5 is a phase tree of spreadspectrum MSK signals;
FIG. 6 illustrates an output of a first matched filter which is matched to cos_{doub} S(n,C);
FIG. 7 illustrates an output of a second matched filter which is matched to sin_{doub} S(n,C);
FIG. 8 is a block diagram of a differentially coherent spreadspectrum MSK receiver of special types of codewords;
FIG. 9 illustrates error rate curves for an average chip phase receiver; and
FIG. 10 illustrates error rate curves for a differentially coherent spreadspectrum MSK receiver.
Reference now is made in detail to the present preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals indicate like elements throughout the several views.
A novel noncoherent MSK receiver structure is disclosed for receiving spreadspectrum MSK modulation. The MSK receiver structure allows CDMA operation because the MSK receiver's front end to the output of the correlators is linear. The nonlinear operation due to noncoherent demodulation follows the correlators.
The primary new implementation requirements for this type of receiver are analogtodigital (A/D) samples into the correlators, four instead of two sets of sample registers, and frequency stability comparable to that for coherent binary phaseshiftkeyed (BPSK) systems.
A set of orthogonal, codewords is presented. "Orthogonal" is used in the sense of zero interuser interference at the output of the receiver. A differentially coherent spreadspectrum MSK receiver also is presented as well as minimum interuser interference conditions in a synchronous code division multiple access (SCDMA) environment with such receivers.
This section presents the conditions for zero interuser interference, and represents the suboptimal noncoherent spreadspectrum MSK receiver with sufficiently simple structure. The set of orthogonal, in the sense of the zero interuser interference at the output of the receiver, codewords is presented. The design of a differentially coherent spreadspectrum MSK receiver also is presented as well as minimum interuser interference conditions in SCDMA with such receivers.
FIG. 1 illustratively shows the model of a synchronous CDMA system with spreadspectrum MSK modems. A plurality of MSK modulators 21, 22, 23 receive data d_{1}. The outputs of the modulators are x_{1} (d_{1}, C^{1}), x_{2} (t, d_{2}, C^{2}), . . . , x_{M} (t_{M}, C^{M}). The outputs are sent over a communications channel, and additive white gaussian noise (AWGN) 24 is added 25 to the signals. The combined signal from the channel are r(t).
A plurality of blocks of receivers, 26, 28, 30 with each receiver having the maximum likelihood receiver, are coupled to a plurality of decision devices 27, 29, 31. Accordingly, the block of maximum likelihood receivers 26 would be coupled to decision device 27. A second linear block of maximum likelihood receivers 28 would be coupled to decision device 29. The M^{th} linear block of maximum likelihood receivers 30 would be coupled to decision device 31.
The spreadspectrum MSK transmitter signal is a constant envelope signal that depends on the whether the data bit "d" is +1 or 1. Assume that for each data bit "d" the N chip sequence into the MSK modulator is given by dC. That is, for a conventional "1" data bit, the chip sequence into the MSK modulator is C, corresponding to d=1, and for a conventional "0" data bit, corresponding to d=1, the chip sequence into the MSK modulator is C. During the time interval when a single data bit "d" is being sent, the constant envelope MSK signal includes the modulation of the N chip sequence dC.
Referring to the model in FIG. 1, there are Musers, each of which are independent. One of the Musers, say user i, sends a ±1 data bit d_{i} by means of spreadspectrum MSK modulation, encoding his information bits d_{i} into C.sup.(i) if d_{i} =1 ("1"), and C.sup.(i) if d_{i} =1("0") Sequence C.sup.(i) includes the symbols
C.sub.n.sup.i =±1, n=o,N1
which are called chips. The transmitted spreadspectrum MSK signal at the output of the modulator is
X.sub.i (t,d,C.sup.(i))=A cos {w.sub.o t+p(t,d.sub.i C.sup.(i))+φ.sub.i } (1)
where ##EQU1## during the time interval nT<t≦(n+1)T
The phase state is defined as ##EQU2## The phase φ_{i} is the unknown phase that is equally likely to be anywhere between 0° and 360°. If this signal x_{i} (t,d_{i} C.sup.(i)) were distorted by Additive White Gaussian Noise (AWGN) n(t) then the maximum likelihood (ML) noncoherent receiver at first calculates ##EQU3## for d=1 and d=1, respectively, where
y(t)=x.sub.i (t,d.sub.i C.sup.(i))+n(t) (4)
and then makes the decision:
Choose the data bit d_{i} to be "1" if and only if ##EQU4## Such receiver is assigned to each user of FIG. 1.
The signal at the input of each receiver is ##EQU5## where n(t) is AWGN.
The signal r(t) at the input of the i^{th} receiver, in addition to the AWGN, also contains the interference noise ##EQU6##
In order to avoid the interference noise influence on the estimation of the data bit d_{i}, the interference noise is eliminated at the output of linear block of the receiver before doing nonlinear operation.
Thus, due to linearity of the first blocks of the receivers, the zero interuser interference conditions for the i^{th} user in a SCDMA system with spreadspectrum MSK modulation (1)(2) are ##EQU7## where d=±1, k=1,M, k≠i In this model, bit and chip synchronization are assumed, but the initial phases of the signals of the different users are arbitrary. Synchronization is assumed also for the receiver.
The conditions in equations 7(a) and 7(b) are simplified by using the signal representation (1), (2), (2a) and well known trigonometrical relationships. Assuming that the d=1, d_{k} =1 yields ##EQU8## Ignoring the last term and the factor of 1/2 and using the cosine relationship yields ##EQU9## Since the last equality holds for any φ_{k} then (8) leads to two conditions ##EQU10## Condition (9a) by using again a cosine relationship leads to ##EQU11##
The value of each the above integrals can be expressed by the value of cos S(n,C), sin S(n,C), cos S(n+1,C) and sin S(n+1,C) regardless of the value of c_{n}. For example, consider the integral in (9c) for an even time interval from nT to (n+1)T, with n being even, and S(n,C(k))=0 or 180°. The integral can be simplified by using the following expressions, which are apparent from the phase state circle consideration of FIG. 2. ##EQU12## By using these expressions, the integral in (9c) can be calculated and instead of (9c) one has ##EQU13## where ##EQU14## is the constant value and here and everywhere cos S(n,C).tbd.cos(0,C)=1
sin S(n,C).tbd.sin(0,C)=0
Analogously, the condition (9b) leads to ##EQU15## where ##EQU16## is the constant value.
Condition b_{i}.sup.(k) (1)=0 leads to the similar (10a), (10b) conditions, but condition a_{i}.sup.(k) (1)=0 leads to two new conditions ##EQU17## For deriving (10c) and (10d), use the relationships cos S(n,C)=cos S(n,C)
sin S(n,C)=sin S(n,C)
The first two conditions (10a), (10b) are the conditions of orthogonality of two arbitrary spreadspectrum MSK signals x(t,C.sup.(i)) and x(t,C.sup.(k)). In particular, the signals of single user x(t,C.sup.(i)) and x(t,C.sup.(i)) are orthogonal if and only if ##EQU18## The condition (10) can be satisfied if and only if C.sup.(i) and C.sup.(k) are chosen with the following properties ##EQU19## or equivalently (12a), (12b), (12c), and (12d) can be written as ##EQU20## respectively. The terms Cos_{doub} S(n,C) and Sin_{doub} S(n,C) mean that in the Cos S(n,C) and Sin S(n,C) the zero components are replaced by their following one's.
For example,
Cos S(n,C)=1 01 01 0 1 0 1 01 0
Cos_{doub} S(n,C)=11111 1 1 1 111 1
Sin S(n,C)=01 0 1 0 1 01 0 1 01
Sin_{doub} S(n,C)=11 1 1 1 111 1 111
For the optimal noncoherent MSK spreadspectrum receiver defined by (3), (4), and (5), the sufficient and necessary zero interuser interference condition on used codewords is given by (12a), (12b), (12c), and (12d) or equivalently by (12e), (12f), (12g), and (12h).
Suboptimal spreadspectrum MSK noncoherent receiver structure for special type of codewords, i.e., orthogonal signals, will now be discussed. The goal is to represent a suboptimal MSK noncoherent receiver which has a simple structure and evaluate the possibilities of the suggested receiver in SCDMA. Assume that the receiver calculates the following values: ##EQU21## Let's allow the transmitter to use only such codewords C.sup.(i) for which ##EQU22##
This receiver, which is called the Average Chip Phase (ACP) receiver, allows the simple structure implementation of FIG. 3. For every n^{th} chip time, the information containing phase p(t,C(i)), see (2) and (2a), varies linearly on time from S(n,C) signal to S(n+1,C). The optimal receiver correlates the received signal with the signal having a phase which varies linearly in the same manner from S(n,C) to S(n+1,C), see (3). The suboptimal ACP receiver correlates the received signal with the signal having a phase which is equal to the average value of the information carrying phase for every n^{th} chip time, namely to (S(n,C)+S(n+1,C))/2, see (13). This ACP receiver can be implemented as in FIG. 3. ##EQU23## Evaluating the value of ##EQU24## in the sum for two successive chips n and n+1, letting n be odd, then, referring to the phase state circle of FIG. 2, ##EQU25## Thus two successive chips in the matched filter (MF) coincide, therefore a matched content is Cos_{doub} S(n,C). Finally it follows that (13) can be realized as in FIG. 3.
When the MSK signal x(t), as defined by (1) and (2) and with φ instead of φ_{i} and ignoring index i, is passed to the input of this receiver then the outputs of the matched filters at the end of the bit interval are: ##EQU26## where ##EQU27## and d is a transmitted data bit.
The decision rule for this receiver is the same rule (5) as for the optimal receiver.
Since the best performance for the noncoherent receiver is achieved by using orthogonal signals, the transmitter can be allowed to use only such codewords C.sup.(i) for which x(t,C.sup.(i)) and x(t,C.sup.(i)) are orthogonal,i.e., for which the condition (11) holds ##EQU28## or equivalently ##EQU29##
The limitation (15) on the used signal with this receiver provides zero for ##EQU30## while ##EQU31## are maximal and vice versa, for the noiseless case. If codeword C.sup.(i) satisfied the limitation (15) then
a(1)=MF.sub.2 (out)MF.sub.3 (out)=2δN cos φ
b(1)=MF.sub.1 (out)+MF.sub.4 (out)=2δN sin φ (16)
a(1)=MF.sub.2 (out)+MF.sub.3 (out)=0
b(1)=MF.sub.1 (out)MF.sub.4 (out)=0, ##EQU32## For transmitted data d=1, see (14).
The ACP receiver can be shown to be suboptimal for orthogonal signals (15) by comparing this receiver with the optimal receiver defined by (3), (4), and (5). If the signal were introduced at the input of the receiver as y(t)=x(t,dC)+n(t), where n(t) is an AWGN signal, then by comparing (3a) and (3b) with (13a) and (13b) it can be seen that the noise at the outputs of both receivers has the same characteristics, but the MSK modulated signal x(t,dC) at the input of the ACP receiver has an amplitude α times larger than the MSK modulated signal at the input of the optimal receiver to produce the same signaltonoise ratio.
Factor α can be found as follows: ##EQU33## which corresponds to 0.9 dB. The loss of 0.9 dB is obtained for the receiver which employs orthogonal signals (15) because, in this case, if transmitted data d=1 and noise were absent, a(1)=b(1)=0 for the ACP receiver, see (16), as well as for the optimal receiver, see (7a). On the other hand, a(1) and b(1) for the ACP receiver are 1.11 times smaller than a(1) and b(1) for the optimal receiver, see (17), if the same signal were at the inputs of both receivers. Because noise behavior on the outputs of both receivers is the same, the ACP receiver provides the same error probability as the optimal receiver if the signal at the input of the ACP receiver had an amplitude 1.11 times larger than the signal at the input of the optimal receiver. Thus loss=20 log 1.11=0.9 dB.
It is not difficult to check, see (14), where cos_{doub} S(n,dC), sin_{doub} S(n,dC) should be substituted by cos_{doub} S(n,dC.sup.(i)), sin_{doub} S(n,dC.sup.(i)) and cos_{doub} S(n,C), sin_{doub} S(n,C) by cos_{doub} S(n,C.sup.(k)), sin_{doub} S(n,C.sup.(k)) that zero interuser interference conditions for SCDMA with a noncoherent MSK suboptimal (0.9 dB) receiver coincide with conditions (10) or (12) derived earlier for the optimal receiver.
As shown in FIG. 3, an optimal noncoherent receiver for demodulating a receivedspreadspectrum OQPSK signal y(t), as defined by equations 13 and 5, is shown comprising first generating means, second generating means, first processing means, second processing means, third processing means, fourth processing means, first inverting means, second inverting means, first combining means, second combining means, third combining means, fourth combining means and deciding means. The first processing means is coupled to the first generating means. The second processing means is coupled to the second generating means. The third processing means is coupled to the first generating means. The fourth processing means is coupled to the second generating means. The first inverting means is coupled to the first processing means, and the second inverting means is coupled to the second processing means. The first combining means is coupled to the first processing means and to the fourth processing means. The second combining means is coupled through the first inverting means to the first processing means, and to the fourth processing means. The third combining means is coupled to the second processing means and to the third processing means. The fourth combining means is coupled through the second inverting means to the second processing means, and to the third processing means. The deciding means is coupled to the first combining means, to the second combining means, to the third combining means, and to the fourth combining means.
The first generating means generates an inphasecomponent signal from the receivedspreadspectrum signal y(t). The second generating means generates a quadraturephasecomponent signal from the receivedspreadspectrum signal y(t). The first processing means processes the inphasecomponent signal using sin_{doub} S(n,C) to generate a first processed signal. The second processing means processes the quadraturephasecomponent signal using sin_{doub} S(n,C) to generate a second processed signal. The third processing means processes the inphasecomponent signal using cos_{doub} S(n,C) to generate a third processed signal. The fourth processing means processes the quadraturephasecomponent signal using cos_{doub} S(n,C) to generate a fourth processed signal. The first inverting means inverts the first processed signal to generate an inverse of the first processed signal. The second inverting means inverts the second processed signal to generate a inverse of the second processed signal.
The first combining means combines the first processed signal with the fourth processed signal to generate a first combined signal. The second combining means combines the inverse of the first processed signal with the fourth processed signal to generate a second combined signal. The third combining means combines the second processed signal with the third processed signal to generate a third combined signal. The fourth combining means combines an inverse of the second processed signal with the third processed signal to generate a fourth combined signal. The deciding means decides or selects an estimate of the data of the receivedspreadspectrum signal y(t), from the first combined signal, the second combined signal, the third combined signal and the fourth combined signal.
In the exemplary arrangement shown in FIG. 3, the first generating means is illustrated, by way of example, as signal generator 41, mixer 42, lowpass filter 43, and integrateanddump circuit 44. The mixer 42 is coupled between the input, the signal generator 41, and the lowpass filter 43. The integrateanddump circuit 44 is coupled to the output of the lowpass filter 43. The first generating means alternatively may be implemented with other types of correlators, a matched filter, surface acoustic wave (SAW) device, or equivalent circuitry, as is well known in the art.
The second generating means is shown as signal generator 41, mixer 47, lowpass filter 48, and integrateanddump circuit 49. The mixer 47 is coupled between the signal generator 41, the lowpass filter 48, and to the input y(t). The integrateanddump circuit 49 is coupled to the output of the lowpass filter 48. The second generating means may be implemented with other types of correlators, a matched filter, surface acoustic wave (SAW) device or equivalent circuitry, as is well known in the art.
By way of example, the first processing means is illustrated as a first matched filter 46 having impulse function sin_{doub} S(n,C). The first matched filter is coupled to the output of the integrateanddump circuit 44. The first processing means alternatively may be implemented using a SAW device, a correlator embodied as a mixer, filter and signal generator, or other circuitry. When using a correlator, the signal generator would generate a signal with sin_{doub} S(n,C).
The second processing means is illustrated as second matched filter 51 having impulse function sin_{doub} S(n,C). The second matched filter 51 is coupled to the output of the integrateanddump circuit 49. The second processing means alternatively may be implemented as a SAW device, a correlator, embodied as a mixer, signal generator and filter, or other circuitry. When using a correlator, the signal generator would generate a signal with sin_{doub} S(n,C).
The third processing means is illustrated with a third matched filter 45 having impulse function cos_{doub} S(n,C). The third matched filter 45 is coupled to the output of the integrateanddump circuit 44. The third processing means alternatively may be implemented as a SAW device, a correlator, embodied as a mixer, filter and signal generator, or other circuitry. When using a correlator, the signal generator would generate a signal with cos_{doub} S(n,C).
The fourth processing means is illustrated by fourth matched filter 50 having impulse function cos_{doub} S(n,C). The fourth matched filter 50 is coupled to the output of the integrateanddump circuit 49. The fourth processing means alternatively may be implemented as a SAW device, a correlator, embodied as a mixer, filter and signal generator, or other circuitry. When using a correlator, the signal generator would generate a signal with cos_{doub} S(n,C).
The first inverting means may be an invertor, or merely an inverting input to the second combining means. The second inverting means may be an invertor, or an inverting input to the fourth combining means. The first combining means, the second combining means, the third combining means and the fourth combining means are illustrated in FIG. 3 as first combiner 53, second combiner 54, third combiner 52, and fourth combiner 55. The first inverting means is shown as an inverting input to the second combiner 54. The second inverting means is shown as an inverting input to the fourth combiner 55. The first combiner 53 is coupled to the output of the first matched filter 46 and to the output of the fourth matched filter 50. The second combiner 54 is coupled to the output of the fourth matched filter 50 and has an inverting input or invertor coupled to the output of the first matched filter 46. The third combiner 52 is coupled to the output of the third matched filter 45 and to the output of the second matched filter 51. The fourth combiner 55 is coupled to the output of the third matched filter 45 and has an inverting input or invertor coupled to the output of the second matched filter 51. The outputs of the first combiner 53, the second combiner 54, the third combiner 52, and the fourth combiner 55 are coupled to the decision device 56.
The generator 41 generates a cosω_{o} t signal and a sinω_{o} t signal. To obtain the inphasecomponent signal, the mixer 42 mixes the receivedspreadspectrum signal y(t) with cosω_{o} t, and the lowpass filter 43 filters the output of the mixer 42. The integrateanddump circuit 44 samples the output of the lowpass filter 43. At the output of the integrateanddump circuit 44 is the inphasecomponent signal of the receivedspreadspectrum signal y(t).
To obtain the quadraturephasecomponent signal, the mixer 47 mixes the receivedspreadspectrum signal y(t) with sinω_{o} t, and the lowpass filter 48 filters the output of the mixer 47. The integrateanddump circuit 49 samples the output of the lowpass filter 48. At the output of the integrateanddump circuit 49 is the quadraturephasecomponent signal of the receivedspreadspectrum signal y(t).
The frequency ω_{o} would be equal to the carrier frequency of the receivedspreadspectrum signal y(t) if the subsequent processing or filtering were at baseband. The frequency ω_{o} would be different from the carrier frequency of the receivedspreadspectrum signal y(t) if the processing or filtering were done at a frequency other than the carrier frequency of the receivedspreadspectrum signal y(t), such as an intermediate frequency, if SAW device were used for the first processing means, the second processing means, the third processing means, and the fourth processing means.
The first matched filter 46 processes or filters the inphasecomponent signal using impulse function sin_{doub} S(n,C) to generate the first processed signal. The second matched filter 51 processes or filters the quadraturephasecomponent signal using impulse function sin_{doub} S(n,C) to generate the second processed signal. The third matched filter 45 processes or filters the inphasecomponent signal using impulse function cos_{doub} S(n,C) to generate the third processed signal. The fourth matched filter 50 processes or filters the quadraturephasecomponent signal using an impulse function cos_{doub} S(n,C) to generate the fourth processed signal. The impulse functions sin_{doub} S(n,C) and cos_{doub} S(n,C) may be approximated for each matched filter to accomplish the same result.
The first combiner 53 combines the first processed signal with the fourth processed signal to generate the first combined signal. The second combiner 54 combines the inverse of the first processed signal with the fourth processed signal to generate the second combined signal. The third combiner 52 combines the second processed signal with the third processed signal to generate the third combined signal. The fourth combiner 55 combines the inverse of the second processed signal with the third processed signal to generate the fourth combined signal.
The decision device 56 decides or selects the estimate data of the receivedspreadspectrum signal y(t) from the first combined signal, the second combined signal, the third combined signal and the fourth combined signal. For the embodiment shown in FIG. 3, a maximum likelihood decision scheme might be used.
As another special case, consider OQPSK. The OQPSK signal can be described by (1), but where p(t,dC) is defined in another manner then for MSK (2). ##EQU34## where ##EQU35##
Such definition of p(t,dC) leads to a spreadspectrum OQPSK signal. The optimal receiver structure is (3) (5), where p(t,dC) is defined above, which coincides with (13). Thus an optimal OQPSK receiver can be implemented as in FIG. 3. The orthogonality conditions remain the same as for MSK signals. The bit error rate curve for orthogonal OQPSK signals coincides with the theoretical curve shown in FIG. 9.
Thus the ACP noncoherent spreadspectrum MSK receiver of FIG. 3 is suboptimal (0.9 dB) and allows SCDMA operation of FIG. 1 with the zero interuser interference condition if each user employs an MSK spread spectrum modulated signal with codewords C.sup.(i), i=1,M, satisfying the conditions (12) and (15).
There can be several methods for choosing C.sup.(i), i=1,M, with properties (12), (15). For example, as nonzero components of cos S(n,C.sup.(i)) i=1,M the rows of a first half of a Hadamard matrix of Sylvester type can be chosen; as nonzero components of sin S(n,C.sup.(i)) i=1,M the rows of the second half of the Hadamard matrix of Sylvester type can be chosen:
Cos S(n,C.sup.(1))=1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
Cos S(n,C.sup.(2))=1 01 0 1 01 0 1 01 0 1 01 0 1
Cos S(n,C.sup.(3))=1 0 1 01 01 0 1 0 1 01 01 0 1
Cos S(n,C.sup.(4))=1 01 01 0 1 0 1 01 01 0 1 0 1
Sin S(n,C.sup.(4))=0 1 0 1 0 1 0 1 01 01 01 01
Sin S(n,C.sup.(1))=0 1 01 0 1 01 01 0 1 01 0 1
Sin S(n,C.sup.(3))=0 1 0 1 01 01 01 01 0 1 0 1
Sin S(n,C.sup.(2))=0 1 01 01 0 1 01 0 1 0 1 01
Corresponding codewords are
C.sup.(1) =111 1 111 11 1 111 1 11
C.sup.(2) =1 1 1 111111111 1 1 1 1
C.sup.(3) =11 1 1 11 1 11 1111 111
C.sup.(4) =1 11 111 1111 11 1 11 1
The number of users M is equal to N/4, in this case, where N is the length of the codewords.
The performance of a spreadspectrum MSK noncoherent receiver can be improved in the model where an unknown phase of the transmitted signal varies slowly from bit to bit. In this case a differentially coherent receiver, which is based on the ACP receiver structure of FIG. 3 is used with changed decision block as shown in FIG. 4.
In the exemplary arrangement shown in FIG. 4, a receiver for demodulating a receivedspreadspectrum signal y(t) is shown comprising first generating means, second generating means, first processing means, second processing means, third processing means, fourth processing means, inverting means, first combining means, second combining means, and deciding means. The first processing means is coupled to the first generating means. The second processing means is coupled to the second generating means. The third processing means is coupled to the first generating means. The fourth processing means is coupled to the second generating means. The inverting means is coupled to the first processing means.
The first combining means is coupled to the second processing means and to the fourth processing means. The first combining means is coupled through the inverting means to the second processing means and to the fourth processing means. The deciding means is coupled to the first combining means and to the second combining means.
The first generating means generates an inphasecomponent signal from the receivedspreadspectrum signal y(t). The second generating means generates a quadraturephasecomponent signal from the receivedspreadspectrum signal y(t). The first processing means processes the inphasecomponent signal using sin_{doub} S(n,C) to generate a first processed signal. The second processing means processes the quadraturephasecomponent signal using sin_{doub} S(n,C) to generate a second processed signal. The third processing means processes the inphasecomponent signal using cos_{doub} S(n,C) to generate a third processed signal. The fourth processing means processes the quadraturephasecomponent signal using cos_{doub} S(n,C) to generate a fourth processed signal. The inverting means inverts the first processing signal to generate a inverse of the first processed signal.
The first combining means combines the second processed signal with the third processed signal to generate a first combined signal. The second combining means combines the inverse of the first processed signal with the fourth processed signal to generate a second combined signal. The deciding means decides or selects from the first combined signal and the second combined signal, an estimate of the data of the receivedspreadspectrum signal y(t). The deciding means may determine an angle from an arctangent of the ratio of the first combined signal and second combined signal, and compare the magnitude of the angle to 90°. The estimate of the data is determined from the comparison.
As illustratively shown in FIG. 4, the first generating means is illustrated, by way of example, as signal generator 41, mixer 42, lowpass filter 43, and integrateanddump circuit 44. The mixer 42 is coupled between the input, the signal generator 41, and the lowpass filter 43. The integrateanddump circuit 44 is coupled to the output of the lowpass filter 43. The first generating means alternatively may be implemented with a matched filter or equivalent circuitry, as is well known in the art.
The second generating means is shown as signal generator 41, mixer 47, lowpass filter 48, and integrateanddump circuit 49. The mixer 47 is coupled between the signal generator 41, the lowpass filter 48, and to the input. The integrateanddump circuit 49 is coupled to the output of the lowpass filter 48. The second generating means may be implemented with a matched filter, as is well known in the art.
By way of example, the first processing means is illustrated as a first matched filter 46 having impulse function sin_{doub} S(n,C). The first matched filter is coupled to the output of the integrateanddump circuit 44. The first processing means alternatively may be implemented using a SAW device, a correlator embodied as a mixer, filter and signal generator, or other circuitry. The signal generator would generate a signal with sin_{doub} S(n,C).
The second processing means is illustrated as second matched filter 51 having impulse function sin_{doub} S(n,C). The second matched filter 51 is coupled to the output of the integrateanddump circuit 49. The second processing means alternatively may be implemented as a SAW device, a correlator embodied as a mixer, signal generator and filter, or other circuitry. The signal generator would generate a signal with sin_{doub} S(n,C).
The third processing means is illustrated with a third matched filter 45 having impulse function cos_{doub} S(n,C). The third matched filter 45 is coupled to the output of the integrateanddump circuit 44. The third processing means alternatively may be implemented as a SAW device, a correlator embodied as a mixer, filter and signal generator, or other circuitry. The signal generator would generate a signal with cos_{doub} S(n,C).
The fourth processing means is illustrated by fourth matched filter 50 having impulse function cos_{doub} S(n,C). The fourth matched filter 50 is coupled to the output of the integrateanddump circuit 49. The fourth processing means alternatively may be implemented as a SAW device, a correlator, embodied as a mixer, filter and signal generator, or other circuitry. The signal generator would generate a signal with cos_{doub} S(n,C).
The inverting means may be an invertor, or merely an inverting input to the second combining means. The first combining means and the second combining means are illustrated as first combiner 58 and second combiner 53. The first combiner 58 is coupled to the output of the second matched filter 51 and to the output of the third matched filter 45. The second combiner 53 is coupled to the output of the fourth matched filter 50 and has an inverting input or invertor coupled to the output of the first matched filter 46. The outputs of the first combiner 58 and the second combiner 53, are coupled to the decision device 56.
The generator 41 generates a cosω_{o} t signal and a sinω_{o} t signal. To obtain the inphasecomponent signal, the mixer 42 mixes the receivedspreadspectrum signal y(t) with cosω_{o} t, and the lowpass filter 43 filters the output of the mixer 42. The integrateanddump circuit 44 samples the output of the lowpass filter 43. At the output of the integrateanddump circuit is the inphasecomponent signal of the receivedspreadspectrum signal y(t).
To obtain the quadraturephasecomponent signal, the mixer 47 mixes the receivedspreadspectrum signal y(t) with sinω_{o} t, and the lowpass filter 48 filters the output of the mixer 47. The integrateanddump circuit 49 samples the output of the lowpass filter 48. At the output of the integrateanddump circuit 49 is the quadraturephasecomponent signal of the receivedspreadspectrum signal y(t).
The first matched filter 46 processes or filters the inphasecomponent signal using impulse function sin_{doub} S(n,C) to generate the first processed signal. The second matched filter 51 processes or filters the quadraturephasecomponent signal using impulse function sin_{doub} S(n,C) to generate the second processed signal. The third matched filter 45 processes or filters the inphasecomponent signal using impulse function cos_{doub} S(n,C) to generate the third processed signal. The fourth matched filter 50 processes or filters the quadraturephasecomponent signal using an impulse function cos_{doub} S(n,C) to generate the fourth processed signal. The impulse functions sin_{doub} S(n,C) and cos_{doub} S(n,C) may be approximated for each matched filter to accomplish the same result.
The first combiner 58 combines the second processed signal with the third processed signal to generate the first combined signal. The second combiner 53 combines the inverse of the first processed signal with the fourth processed signal to generate the second combined signal.
The decision device 56 decides or selects the estimate data of the receivedspreadspectrum signal y(t) from the first combined signal and the second combined signal. For the embodiment shown in FIG. 4, an angle is determined from the arctangent 61 of a ratio of the first combined signal and the second combined signal. The magnitude of the angle is compared 62 to determine if the magnitude is greater or less than 90°. The estimate data are selected or determined from this comparison.
In the case of full phase uncertainty the best performance for the spreadspectrum MSK modem was achieved for orthogonal signals. In the case of differentially coherent implementation, the best performance would be expected for antipodal signals as the representation of differentially encoded data bits "0" and "1". To keep the phase continuity uninterrupted at the transition from bit to bit, signals which are "almost" antipodal are used; "almost" antipodal means that the signals used are antipodal in every chip duration excluding the first one and the last one, as shown in the phase tree in FIG. 5.
C.sub.1 =1 11 1 1111 (18)
C.sub.0 =1 11 1 111 1
The phase tree of FIG. 5 shows the phase difference between signals corresponding to differentially encoded data bits "1" and "0" is 180° during every chip time except the first chip time and the last chip time. This can be achieved if the first C_{0} and the last C_{N1} chip component of C_{1} and C_{0} are opposite and the remaining components are the same (18). It can be seen also that
Sin S(n,C.sub.1)=Sin S(n,C.sub.0), n=0,N1
Cos S(n,C.sub.1)=Cos S(n,C.sub.0), n=1,N1 (19)
Cos S(n,C.sub.1)=Cos S(n,C.sub.0), n=0,n=N
The differentially coherent receiver estimates the carrier phase φ_{k} after transmission of the k^{th} bit to compare it with estimation of φ_{k1} by processing the outputs of a(1), b(1) which are
a.sub.k (1)=2δN cos φ.sub.k (20a)
b.sub.k (1)=2δN sin φ.sub.k,
if d=1 is transmitted and
a.sub.k (1)=2δN cos φ.sub.k +4δ(cos φ.sub.k sin φ.sub.k) (20b)
b.sub.k (1)=2δN sin φ.sub.k +4δ(cos φ.sub.k +sin φ.sub.k)
if d=0 is transmitted as k^{th} bit, e.g., the noiseless case, where ##EQU36## (see (14) and (16), where C and C must be changed by C_{1} and C_{0} for differentially encoded data bits "1" and "0", respectively: So,the decision is as follows:
Choose the data bit d_{i} to be "0" if and only if .linevert split.φkφ k1.linevert split.<90° and vice versa.
The performance of the differentially coherent spreadspectrum MSK receiver of FIG. 4 with almost antipodal signals was investigated by a simulation model in which it was assumed that there was no transmitter carrier phase change from chip to chip within each bit, but at transition from the k^{th} bit to the k+1^{th} bit, this phase φ_{k} can change its value from φ_{k} to φ_{k+1} in the manner that φ_{k+1} takes equally likely values in the phase region
{φkΔ;φk+Δ} where Δ=0° or 10° or 20°, (21)
i.e., dealing with a first order Markov process, φ_{o} is equally likely to be anywhere between 0° and 360°. The simulation results are presented in a following section.
Signals x(t,C_{1}) and x(t,C_{0}) are not perfectly antipodal because of the first chips and last chips. The effect of the first chips and last chips can be escaped if, in the receiver of FIG. 4, instead of MF1, MF2, MF3, MF4, the shortened matched filters of length N2 excluding first cos_{doub} (0,C), sin_{doub} (0,C) and last cos_{doub} (N,C), sin_{doub} (N,C) components of the matched filters are used. Then instead of (20a) (20b), one has:
a.sub.k (1)=2δ(N2) cos φ.sub.k
b.sub.k (1)=2φ(N2) sin φ.sub.k,
if d=1 is transmitted and
a.sub.k (1)=2δ(N2) cos φ.sub.k
b.sub.k (1)=2δ(N2) sin φ.sub.k
if d=0 were transmitted as the k^{th} bit, e.g., the noiseless case, where ##EQU37##
In order to simplify the structure of the differentially coherent MSK spreadspectrum receiver of FIG. 4, consider only such codewords C for which nonzero components of cos S(n,C) and sin S(n,C) coincide. Then cos_{doub} S(n,C) and sin_{doub} S(n,C) can be written as
cos.sub.doub S(n,C)=1 a.sub.1 a.sub.1 a.sub.2 a.sub.2 . . . a.sub.N1 a.sub.N1 1 (22)
sin.sub.doub S(n,C)=a.sub.1 a.sub.1 a.sub.2 a.sub.2 a.sub.3 . . . a.sub.N1 1 1
FIGS. 6 and 7 illustrate that the output of the third matched filter 45 which is matched to cos_{doub} S(n,C) and this case can be obtained by picking up the output of the first matched filter 46 (sin_{doub} S(n,C)) at one chip time instance earlier. Some distortion is possible for the first and last chips, but as we have noted above, these two chips can be excluded by using shortened matched filters.
In FIGS. 6 and 7, the mean row of both tables includes the value of samples at the integrator output. The upper row is a content of the first matched filter 46 and the lower row is a content of the third matched filter 46. As shown, the matched filtering procedure in the first matched filter 46 and the third matched filter 45 differs by one chip shift and therefore the realization of a simplified differentially coherent spreadspectrum MSK receiver in the case when sin_{doub} S(n,C) and cos_{doub} S(n,C) coincide with an accuracy of one chip shift can be implemented as shown in FIG. 8, where D denotes the one chip delay element.
FIG. 8 shows a differentially coherent spreadspectrum MSK receiver for special type of codewords. If in practice it is necessary to accumulate the value of a(1) and b(1) in any window, then the delay elements can be eliminated. By eliminating the delay elements, the operation of adding and subtracting of the matched filters in FIG. 8 can also be eliminated, as corresponding to just rotation on 45°, resulting in derivation of the usual differentially coherent receiver for DBPSK signals. It can be seen that if codeword C had the structure (22), then at every even chip time the mean value of the information carrying phase of the MSK signal would be φ+45° or φ+45°+180°, which roughly corresponds to BPSK signals.
As shown in FIG. 8, a differentially coherent spreadspectrum MSK receiver for demodulating a receivedspreadspectrum signal y(t) is shown comprising first generating means, second generating means, first processing means, second processing means, first delaying means, second delaying means, inverting means, first combining means, second combining means, and deciding means. The first processing means is coupled to the first generating means. The second processing means is coupled to the second generating means. The first delaying means is coupled to the first processing means. The second delaying means is coupled to the second processing means. The inverting means is coupled to the second processing means. The second combining means is coupled to the first processing means and to the second delaying means. The first combining means is coupled through the inverting means to the second processing means, and to the first delaying means. The deciding means is coupled to the first combining means and to the second combining means.
The first generating means generates an inphasecomponent signal from the receivedspreadspectrum signal y(t). The second generating means generates a quadraturephasecomponent signal from the receivedspreadspectrum signal y(t). The first processing means processes the inphasecomponent signal using sin_{doub} S(n,C) to generate a first combined signal. The second processing means processes the quadraturephasecomponent signal using sin_{doub} S(n,C) to generate a second combined signal. The inverting means inverts the second processed signal to generate an inverse of the second combined signal.
The first combining means combines a delayed version of the first processed signal with the inverse of the second processed signal to generate a first combined signal. The second combining means combines the first processed signal with a delayed version of the second processed signal to generate a second combined signal. The deciding means decides or selects an estimate of the data of the receivedspreadspectrum signal y(t), from the first combined signal and the second combined signal.
Referring to FIG. 8, the first generating means is illustrated, by way of example, as signal generator 41, mixer 42, lowpass filter 43, and integrateanddump circuit 44. The mixer 42 is coupled between the input, the signal generator 41, and the lowpass filter 43. The integrateanddump circuit 44 is coupled to the output of the lowpass filter 43. The first generating means alternatively may be implemented with a matched filter or equivalent circuitry, as is well known in the art.
The second generating means is shown as signal generator 41, mixer 47, lowpass filter 48, and integrateanddump circuit 49. The mixer 47 is coupled between the signal generator 41, the lowpass filter 48, and to the input. The integrateanddump circuit 49 is coupled to the output of the lowpass filter 48. The second generating means may be implemented with a matched filter, or equivalent circuit, as is well known in the art.
By way of example, the first processing means is illustrated as a first matched filter 45 having impulse function sin_{doub} S(n,C). The first matched filter is coupled to the output of the integrateanddump circuit 44. The first processing means alternatively may be implemented using a SAW device, a correlator embodied as a mixer, filter and signal generator, or other circuitry. The signal generator would generate a signal with sin_{doub} S(n,C).
The second processing means is illustrated as second matched filter 50 having impulse function sin_{doub} S(n,C). The second matched filter 50 is coupled to the output of the integrateanddump circuit 49. The second processing means alternatively may be implemented as a SAW device, a correlator, embodied as a mixer, signal generator and filter, or other circuitry. The signal generator would generate a signal with sin_{doub} S(n,C).
The first delaying means may be a delay device 66 which uses circuitry, or other means to accomplish delay. The second delaying means may be a delay device 67, which uses circuitry or other means to effect delay.
The inverting means may be an invertor, or merely an inverting input to the first combining means. The first combining means, and the second combining means are illustrated as first combiner 63 and second combiner 64. The first combiner 63 is coupled through the delay device 66 to the output of the first matched filter 45, and has an inverting input or invertor coupled to the output of the second matched filter 50. The second combiner 64 is coupled through the second delay device 67 to the output of the second matched filter 50 and to the output of the first matched filter 45. The outputs of the first combiner 63 and the second combiner 64 are coupled to the decision device 56.
The generator 41 generates a cosω_{o} t signal and a sinω_{o} t signal. To obtain the inphasecomponent signal, the mixer 42 mixes the receivedspreadspectrum signal y(t) with cosω_{o} t, and the lowpass filter 43 filters the output of the mixer 42. The integrateanddump circuit 44 samples the output of the lowpass filter 43. At the output of the integrateanddump circuit is the inphasecomponent signal of the receivedspreadspectrum signal y(t).
To obtain the quadraturephasecomponent signal, the mixer 47 mixes the receivedspreadspectrum signal y(t) with sinω_{o} t, and the lowpass filter 48 filters the output of the mixer 47. The integrateanddump circuit 49 samples the output of the lowpass filter 48. At the output of the integrateanddump circuit 49 is the quadraturephasecomponent signal of the receivedspreadspectrum signal y(t).
The first matched filter 45 processes or filters the inphasecomponent signal using impulse function sin_{doub} S(n,C) to generate the first processed signal. The second matched filter 50 processes or filters the quadraturephasecomponent signal using impulse function sin_{doub} S(n,C) to generate the second processed signal. The impulse function sin_{doub} S(n,C) may be approximated for each matched filter to accomplish the same result.
The first combiner 63 combines a delayed version of the first processed signal with the inverse of the second processed signal to generate the first combined signal. The second combiner 64 combines a delayed version of the second processed signal with the first processed signal to generate the second combined signal.
The decision device 56 decides or selects the estimate data of the receivedspreadspectrum signal y(t) from the first combined signal and the second combined signal. For the embodiment shown in FIG. 8, an angle is determined from the arctangent 61 of a ratio of the first combined signal to the second combined signal. The magnitude of the angle is compared 62 to determine if the magnitude is greater or less than 90°. The estimate data are selected or determined from this comparison.
In SCDMA in which the differentially coherent spreadspectrum MSK modem system signals assigned to each user are not perfectly antipodal, CDMA operation with zero interuser interference is virtually impossible, but interference noise can be reduced to a sufficiently insignificant level small in comparison with intended signal energy so that zero interuser interference a_{i}.sup.(k) (1)=0, b_{i}.sup.(k) (1)=0 (see 7a, 7b only with d=1) can be derived for a differentially coherent receiver with shortened matched filter by excluding the first and the last chips of the matched filter. The minimum interuser interference conditions, with usual matched filters, or the zero interuser interference conditions, with a shortened matched filter, can be written as follows (see (10a) (10b) or (14)): ##EQU38##
Recall that in an SCDMA system with a noncoherent spreadspectrum MSK modem, each user was assigned orthogonal signals for data "1" and "0". In an SCDMA system with a differentially coherent spreadspectrum MSK modem, these two orthogonal signals can be assigned to two different users. Therefore the number of orthogonal users can be doubled. The noncoherent receiver in FIG. 3 can serve two users, each of whom are employing almost antipodal signals C_{1}.sup.(i), C_{2}.sup.(j) and C_{1}.sup.(j),C_{2}.sup.(j) for which cos S(n,C_{1}.sup.(i))=cos S(n, C_{1}.sup.(j)) sin S(n, C_{1}.sup.(i))=sin S(n, C_{1}.sup.(j)). In this case data detection of one user can be implemented by using a(1) b(1) outputs and the data detection of the second user can be implemented by using a(1) b(1) outputs of the receiver shown in FIG. 3 to calculate the phase φ value.
If the users employ codewords with properties (22) and a corresponding differentially coherent receiver has the structure shown in FIG. 8, then the minimum interuser interference conditions are (see (23a), (23b) with (22)): ##EQU39##
In this section the performance analysis of the noncoherent spreadspectrum MSK receiver and errorrate curves are given. The performance measurement of the MSK receiver under AWGN was implemented by computer simulation using MonteCarlo techniques. To simulate the effect of channel noise, the independent identically distributed Gaussian variables with zero mean and variance VAR were added to noisefree integrator or lowpass filter LPF outputs at sampling instance in inphase and quadrature arms, see FIG.3. At the receiver frontend the data bit "0" is represented by spreadspectrum MSK signal x(t,C) and the data bit "1" is represented by x(t,C) (1), where 64chip codeword C, to provide the orthogonality of x(t,C) and x(t,C), was chosen in accordance with limitation (15): ##EQU40## When the samples were taken after the integrator to transfer the BER vs. VAR to BER vs. E_{b} /N_{o}, the following relationships were used: ##EQU41## where T is a chip duration, A is the amplitude of the MSK signal and N is the number of chips. ##EQU42## where E{.} denotes math expectation and N_{o} is the onesided spectral density of white noise.
From these relationships it follows that E_{b} /N_{o} =80/VAR, because in the simulation N=64, T=π/2, A=2. When samples were taken after the low pass filter and without an integrator, then the E_{b} /N_{o} =NWT/VAR, where W is an equivalent noise bandwidth of the low pass filter. The low pass filter was not simulated, ignoring its effect on the baseband noisefree signal, but it was assumed that because of the good spectral properties of the MSK signal, the approximation W=1.25/T is valid for two samples per chip time, and W=2/T for four samples per chip time. As a result of computer simulation, the following performance curves are plotted in FIG. 9.
As used in FIG. 9, "theoretical curve" illustrates the performance of the optimum noncoherent receiver (BER=0.5 exp(0.5 Eb/No). The "ACP" curve illustrates the performance of the ACP receiver. As seen, there is a degradation of about 1 dB compared to the optimum receiver. Synchronous 3bit and 8bit samples with AGC, give practically the same result as the ACP receiver.
The "3 bit async" curve illustrates the performance when 3bit samples of integrator output were taken asynchronously within T/2. There is degradation of about 0.8 dB compared to the ACP receiver.
The "3 bit 2 samples" curve illustrates the performance of the receiver with asynchronous 3bit samples sampled two times during the chip time just after the low pass filter. There is degradation of about 1 dB compared to the ACP receiver.
The "1 bit sync" curve illustrates the performance when 1bit samples of integrator output are taken synchronously at the end of every chip time. There is degradation about 2 dB compared to the ACP receiver. The "1 bit async" curve illustrates the performance when 1bit samples of integrator output are taken asynchronously within T/2. There is degradation of about 3 dB compared to the ACP receiver.
The "1 bit 2 samples" curve illustrates the performance of the receiver with asynchronous 1bit samples sampled two times during the chip time just after the low pass filter. There is degradation of about 3.5 dB compared to the ACP receiver.
Performance measurement of the differentially coherent MSK receiver, shown in FIG. 4, under AWGN was implemented by computer simulation, in the same manner as was the noncoherent MSK receiver. As the data bit representation, the antipodal spreadspectrum MSK signal has been used ((19),N=64). As a result of computer simulation, the following curves are plotted in FIG. 10.
As used in FIG. 10, "theoretical curve" illustrates the performance of differentially coherent PSK signals (BER=0.5 exp(E_{b} /N_{o}). The "Diff ACP(0)" curve illustrates the performance of the differentially coherent receiver when relative phase instability from bit to bit Δ=0(see (21)).
The "Diff ACP(10)" curve illustrates the performance of the differentially coherent receiver when relative phase instability from bit to bit Δ=10(see (21)).
The "Diff ACP(20)" curve illustrates the performance of the differentially coherent receiver when relative phase instability from bit to bit Δ=20(see (21)).
The "1 bit 2 samples" curve illustrates the performance of the differentially coherent receiver with asynchronous 1bit samples sampled two times during the chip time just after the low pass filter.
The "1 bit integrator" curve illustrates the performance when 1bit samples of integrator output are taken synchronously at the end of every chip time.
The "3 bit 2 samples" curve illustrates the performance of the differentially coherent receiver with asynchronous 3bit samples sampled two times during the chip time just after the low pass filter.
The "1 bit 4 samples" curve illustrates the performance of the differentially coherent receiver with asynchronous 1bit samples sampled four times during the chip time just after the low pass filter coinciding with the "1 bit integrator" curve. It should be noted that synchronous 3bit samples with AGC give practically the same result as "Diff ACP(0)", "Diff ACP(10)", "Diff ACP(20)" correspondingly. Note also that integrator output sampled asynchronously leads to about 1 dB loss. Comparing the curves plotted in FIG. 10 with the curves plotted in FIG. 9 shows that the differentially spreadspectrum MSK receiver has an energetic gain of 2.52.8 dB compared with the noncoherent spreadspectrum MSK ACP receiver shown in FIG. 4.
It will be apparent to those skilled in the art that various modifications can be made to the MSK spreadspectrum receiver of the instant invention without departing from the scope or spirit of the invention, and it is intended that the present invention cover modifications and variations of the MSK spreadspectrum receiver provided they come within the scope of the appended claims and their equivalents.
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